The present invention relates to an optical system of an optical neural network model for parallel data processing.
The output y.sub.i of a second-order neural network where all inputs are connected in pairs, is given by ##EQU1## where x.sub.j, x.sub.k are the same input vector of length N, w.sub.ijk is a weight matrix, and F.sub.Th is a threshold function. When w.sub.ijk values are suitably adjusted during a training stage, then the binary output y.sub.i can differentiate between two possible input classes. The equation (1) is disclosed in Applied Optics, Vol. 26, No. 23, pp 4972-4978, (1987).
This system can be made invariant to a functional transformation of the input by imposing certain on the weight matrix w.sub.ijk, which reflect the symmetry of the particular transformation. The case of invariance to the geometric operations of scaling and translation may be achieved by the condition that EQU w.sub.ijk =w.sub.ij'k' if j-k=j'-k' (2)
Thus all elements of the set x.sub.j x.sub.k where j-k=constant are multiplied by the same weight.
A general scheme for optical implementation of this model has been outlined previously. Particular optical architectures for calculation of the auto-correlation matrix have also been described previously, in Applied Optics, Vol. 21, No. 12, pp 2089-2090, (1982). However, these architectures are complex.